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http://dx.doi.org/10.3795/KSME-A.2012.36.7.805

Improvement of the Convergence Capability of a Single Loop Single Vector Approach Using Conjugate Gradient for a Concave Function  

Jeong, Seong-Beom (Dept. of Mechanical Engineering, Hanyang Univ.)
Lee, Se-Jung (Dept. of Mechanical Engineering, Hanyang Univ.)
Park, Gyung-Jin (Dept. of Mechanical Engineering, Hanyang Univ.)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.36, no.7, 2012 , pp. 805-811 More about this Journal
Abstract
The reliability based design optimization (RBDO) approach requires high computing cost to consider uncertainties. In order to reduce the design cost, the single loop single vector (SLSV) approach has been developed for RBDO. This method can reduce the cost in calculating deign sensitivity by elimination of the nested optimization process. However, this process causes the increment of the instability or inaccuracy of the method according to the problem characteristics. Therefore, the method may not give accurate solution or the robustness of the solution is not guaranteed. Especially, when the function is concave, the process frequently diverges. In this research, the concept of the conjugate gradient method for unconstrained optimization is utilized to develop a new single loop single vector method. The conjugate gradient is calculated with gradient directions at the most probable points (MPP) of previous cycles. Mathematical examples are solved for the verification of the proposed method. The numeri cal performances of the obtained results are compared to those of other RBDO methods. The SLSV approach using conjugate gradient is not greatly influenced by the problem characteristics and improves its convergence capability.
Keywords
Reliability-Based Design Optimization; Single Loop Single Vector Approach; Conjugate Gradient Method;
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